Show that all vectors in the vector field F(y,v)=(v,-y) are tangent to circles centered at the origin.
The hint I have is I can use slopes or dot product: I just need some help on how to use them.
Thanks in advance.
I'm gonna' give this a whirl alright. So the equation of a circle is:
differentiating:
or:
or parametrically:
and thus:
Also, you've got to get Mathematica or something else and just plot these to see globally what's happening. In Mathematica 7, you could use:
StreamPlot[{-x,y},{x,-3,3},{y,-3,3}]
ain't that simple or what?